Modelling and Investigation of Drug and Immune Therapies for Cancer

Abstract

There is much evidence in the literature supporting the hypothesis that immune cells affect the tumour cells. For example, Mattes et al, show that the tumour (i.e., B16-OVA melanoma) is eliminated by Th1 cells, but Th2 cells reduce the size of tu- mour (i.e., not eliminate the tumour cells). However, Xie et al show that the tumour B16 cells are eliminated by Th1 cells. Moreover, Kobayashi et al show that the growth of B16-F10 cells is associated with a large number of Th2 cells. Also, Chen et al show the growth of B16 melanoma cells is associated with a shift from anti-tumour M1 macrophages to pro-tumour M2 macrophages. Thus, there are contra- dictory experimental results on the interactions between the tumour and the immune system, and the biological mechanisms behind these results are still poorly understood. Furthermore, chemotherapy drugs affect not only cancer cells but also immune cells.

In this thesis, we start with a simple model for the interactions between cancer cells and a chemotherapy drug (Cyclophosphamide), and use it to confirm (in combination with experimental data for tumour growth) that Cyclophosphamide has nonlinear drug decay.

The second investigation presents a mathematical model to illustrate the dynamics of immune cells both in the absence and presence of cancer. We show that the tumour is eliminated in the presence of type-I or type-II or a mix of type-I and type-II cytokines, and the tumour grows in the presence of type-II cytokines.

The third investigation involves a mathematical model of the drug effect on the tumour and immune interaction. We show that tumour growth is delayed when the drug is injected before the switch between the Th1 and Th2 cells that dominate the immune response. However, tumour grows faster when the drug is injected after this switch between the Th1 an Th2 cells. A more significant effect of the drug was observed when we assumed that drug injection occurred before the switch between M1 and M2 cells (i.e., before the switch between Th1 and Th2 cells) and this lead to a significant reduction in tumour size as a result of the decrease in the M2 cells.

In our final investigation, we develop a PDE model for the spatial interactions between a chemotherapy drug and cancer cells, and calculate analytically the speed at which the tumour invades the domain (in a travelling wave manner). Moreover, we present a spatial model for the interaction between a chemotherapy drug, cancer cells and macrophages, and we investigate the speed at which the tumour invades the domain (in a travelling wave manner).